MinT - Best Known (154, 154+48, s)-Nets in Base 4

Best Known (154, 154+48, s)-Nets in Base 4

(154, 154+48, 1036)-Net over F₄ — Constructive and digital

Digital (154, 202, 1036)-net over F₄, using

4² times duplication [i] based on digital (152, 200, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 50, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(154, 154+48, 2392)-Net over F₄ — Digital

Digital (154, 202, 2392)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+48, 381555)-Net in Base 4 — Upper bound on s

There is no (154, 202, 381556)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 317686 871872 246694 064339 359810 848980 153065 488666 130220 632800 201611 998773 008991 648092 004142 033390 161960 224020 097741 591764 > 4²⁰² [i]